Finite Group Databasebeta

← #21448830

Subgroups — #21448830

Order 7808.

788 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519749C211yesmaximal, characteristic
2C2×D4×Dic61C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊D61C211yesmaximal, characteristic, complemented
4C2×#14519737C211yesmaximal, characteristic, complemented
5C22×#11758196C211yesmaximal, characteristic, complemented
6#16839662C211yesmaximal, characteristic, complemented
7#16839659C211yesmaximal, characteristic, complemented
8#16839656C211yesmaximal, characteristic, complemented
9#16839651C211yesmaximal, characteristic, complemented
10#16839639C211yesmaximal, characteristic, complemented
11#16839636C211yesmaximal, characteristic, complemented
12#16839634C211yesmaximal, characteristic, complemented
13#16839613C211yesmaximal, characteristic, complemented
14C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
15C61×#386C211yesmaximal, characteristic, complemented
16C22×C22⋊D61C2211yescharacteristic
17C22×C22⋊D61C2211yescharacteristic
18C23×Dic61C2211yescharacteristic
19C23×Dic61C2211yescharacteristic
20C23×Dic61C2211yescharacteristic
21C22×C4×D61C2211yescharacteristic
22#14519749C418yescomplemented
23D4×Dic61—24no—
24C4×C22⋊D61—24no—
25#14519737—24no—
26C2×C4⋊Dic61C2211yescharacteristic
27C2×#11758196—24no—
28C2×#11758196C2211yescharacteristic
29C2×#11758196C2211yescharacteristic
30C2×#11758196C2211yescharacteristic
31C2×#11758196C2211yescharacteristic
32C2×#11758196C2211yescharacteristic
33C2×#11758196C2211yescharacteristic
34C2×C22⋊Dic61C2211yescharacteristic
35C2×C22⋊Dic61C2211yescharacteristic
36C2×C22⋊Dic61C2211yescharacteristic
37C2×#11758198C2211yescharacteristic
38C2×#11758198C2211yescharacteristic
39C2×#11758198C2211yescharacteristic
40C2×#11758198C2211yescharacteristic
41C2×C4×Dic61C2211yescharacteristic
42C2×C4×Dic61C2211yescharacteristic
43C2×C4×Dic61C2211yescharacteristic
44C2×C4×Dic61C2211yescharacteristic
45#14519684C2211yescharacteristic
46#14519684C2211yescharacteristic
47#14519684C2211yescharacteristic
48#14519684C2211yescharacteristic
49C22×D4×C61C2211yescharacteristic
50C23×C4×C61C2211yescharacteristic
51C2×C22⋊C4×C61C2211yescharacteristic
52C2×C22⋊C4×C61C2211yescharacteristic
53C2×C22⋊C4×C61C2211yescharacteristic
54#95×C61C2211yescharacteristic
55#95×C61C2211yescharacteristic
56C24×C61C2311yescharacteristic
57C24×C61C2311yescharacteristic
58C23×D61C2311yescharacteristic
59C2×D4×C61—22no—
60C2×D4×C61—22no—
61C2×D4×C61C2×C414yescomplemented
62C22×C4×C61—22no—
63C22×C4×C61—22no—
64C22×C4×C61—41no—
65C22×C4×C61C2311yescharacteristic
66C22×C4×C61C2311yescharacteristic
67C22×C4×C61C2311yescharacteristic
68C22×C4×C61C2311yescharacteristic
69C22×C4×C61C2311yescharacteristic
70C2×C22⋊D61—22no—
71C2×C22⋊D61—22no—
72C2×C22⋊D61—22no—
73C2×C22⋊D61—22no—
74C2×C22⋊D61C2×C414yescomplemented
75C2×C22⋊D61C2×C414yescomplemented
76C22×Dic61—22no—
77C22×Dic61—22no—
78C22×Dic61—22no—
79C22×Dic61—22no—
80C22×Dic61—22no—
81C22×Dic61—22no—
82C22×Dic61—41no—
83C22×Dic61—41no—
84C22×Dic61C2×C414yescomplemented
85C22×Dic61C2311yescharacteristic
86C22×Dic61C2311yescharacteristic
87C22×Dic61C2311yescharacteristic
88C22×Dic61C2311yescharacteristic
89C22×Dic61C2311yescharacteristic
90C22×Dic61C2311yescharacteristic
91C22×Dic61C2311yescharacteristic
92C2×C4×D61—22no—
93C2×C4×D61—22no—
94C2×C4×D61—41no—
95C22⋊C4×C61—22no—
96C22⋊C4×C61—22no—
97C22⋊C4×C61—41no—
98C22⋊Dic61—22no—
99C22⋊Dic61C2×C414yescomplemented
100C22⋊Dic61D414yescomplemented
101#11758198—22no—
102#11758198—22no—
103#11758198—41no—
104#11758198C2×C414yescomplemented
105C4⋊Dic61—22no—
106#11758196—22no—
107#11758196—22no—
108#11758196—22no—
109#11758196—22no—
110#11758196C2×C414yescomplemented
111#11758196D414yescomplemented
112C4×Dic61—22no—
113C4×Dic61—22no—
114C4×Dic61—22no—
115C4×Dic61—22no—
116C23×C61—21no—
117C23×C61—21no—
118C23×C61—21no—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61—21no—
122C23×C61—21no—
123C23×C61—21no—
124C23×C61—21no—
125C23×C61—21no—
126C23×C61C22×C412yes—
127C23×C61C22×C412yes—
128C23×C61C2×D412yes—
129C23×C61#4112yes—
130C23×C61C2411yescharacteristic
131C22×D61—21no—
132C22×D61—21no—
133C22×D61—21no—
134C22×D61—21no—
135C22×D61—21no—
136C22×D61—21no—
137C22×D61C22×C412yes—
138D4×C61—28no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—21no—
152C2×C4×C61—44no—
153C2×C4×C61C22×C412yes—
154C2×C4×C61C2×D412yes—
155C22⋊D61—28no—
156C22⋊D61—28no—
157C2×Dic61—21no—
158C2×Dic61—21no—
159C2×Dic61—21no—
160C2×Dic61—21no—
161C2×Dic61—21no—
162C2×Dic61—21no—
163C2×Dic61—21no—
164C2×Dic61—21no—
165C2×Dic61—21no—
166C2×Dic61—21no—
167C2×Dic61—28no—
168C2×Dic61—21no—
169C2×Dic61—21no—
170C2×Dic61—21no—
171C2×Dic61—44no—
172C2×Dic61—44no—
173C2×Dic61C22×C412yes—
174C2×Dic61C22×C412yes—
175C2×Dic61C22×C412yes—
176C2×Dic61C2×D412yes—
177C2×Dic61C2×D412yes—
178C2×Dic61C2×D412yes—
179C2×Dic61C2×D412yes—
180C2×Dic61#4112yes—
181C4×D61—44no—
182C22×C61—22no—
183C22×C61—22no—
184C22×C61—22no—
185C22×C61—22no—
186C22×C61—22no—
187C22×C61—22no—
188C22×C61—22no—
189C22×C61—22no—
190C22×C61—22no—
191C22×C61—41no—
192C22×C61—41no—
193C22×C61—41no—
194C22×C61—41no—
195C22×C61C4×D414yescomplemented
196C22×C61C23×C411yescharacteristic
197C22×C61C22×D411yescharacteristic
198C22×C61C22×D411yescharacteristic
199C22×C61C2×#4111yescharacteristic
200C22×C61C2×#4111yescharacteristic
201C22×C61H(5,𝔽2)11yescharacteristic
202C22×C612−1+411yescharacteristic
203C2×D61—22no—
204C2×D61—22no—
205C2×D61—22no—
206C2×D61—41no—
207C2×D61—41no—
208C2×D61—41no—
209C2×D61—41no—
210C4×C61—22no—
211C4×C61—22no—
212C4×C61—41no—
213C4×C61—41no—
214C4×C61—41no—
215Dic61—22no—
216Dic61—22no—
217Dic61—22no—
218Dic61—22no—
219Dic61—22no—
220Dic61—41no—
221Dic61C4×D414yescomplemented
222#2361—611nomaximal, Sylow
223C2×C61—24no—
224C2×C61—42no—
225C2×C61C2×C4×D411yescharacteristic
226C2×C61C2×C4×D411yescharacteristic
227C2×C61#52011yescharacteristic
228C2×C61D4211yescharacteristic
229C2×C61#54711yescharacteristic
230C2×C61#54811yescharacteristic
231C2×C61#55311yescharacteristic
232D61—42no—
233C2×#121—611no—
234C2×C4×D4—611no—
235C2×C4×D4—611no—
236C2×C4×D4—611no—
237C22×C4⋊C4—611no—
238#390—611no—
239#389—611no—
240#388—611no—
241#388—611no—
242#386—611no—
243#386D6111yescharacteristic, complemented
244#385—611no—
245#385—611no—
246C4×C4⋊C4—611no—
247C4×C22⋊C4—611no—
248C61#236111yescharacteristic, complemented, Sylow
249C22×D4—611no—
250C22×D4—611no—
251C22×D4C2×D6111yescharacteristic
252C23×C4—611no—
253C23×C4—611no—
254C23×C4—611no—
255C23×C4—611no—
256C23×C4C2×D6111yescharacteristic
257#121—618no—
258C4×D4—1224no—
259C4×D4—1224no—
260C4×D4—1224no—
261C2×C4⋊C4—611no—
262C2×C4⋊C4—611no—
263C2×C4⋊C4—611no—
264C2×C4⋊C4—611no—
265C2×C4⋊C4—611no—
266C2×C4⋊C4—611no—
267C2×C4⋊C4—611no—
268C2×C4⋊C4—1224no—
269C2×C22⋊C4—611no—
270C2×C22⋊C4—611no—
271C2×C22⋊C4—611no—
272C2×C22⋊C4—611no—
273C2×C22⋊C4—611no—
274C2×C22⋊C4—611no—
275C2×C22⋊C4—611no—
276C2×C22⋊C4C2×D6111yescharacteristic
277C2×C22⋊C4C2×D6111yescharacteristic
278C2×C22⋊C4C2×D6111yescharacteristic
279C2×C42—611no—
280C2×C42—611no—
281C2×C42—611no—
282C2×C42—611no—
283#95—611no—
284#95—611no—
285#95—611no—
286#95—611no—
287#95C2×D6111yescharacteristic
288#95C2×D6111yescharacteristic
289C24—611no—
290C24C22×D6111yescharacteristic
291C24C22×D6111yescharacteristic
292C2×D4—22no—
293C2×D4—22no—
294C2×D4—614no—
295C2×D4—614no—
296C2×D4—1222no—
297C2×D4—1222no—
298C2×D4—1222no—
299C2×D4—1222no—
300C2×D4C4×D6114yescomplemented
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—41no—
304C22×C4—611no—
305C22×C4—614no—
306C22×C4—611no—
307C22×C4—611no—
308C22×C4—611no—
309C22×C4—611no—
310C22×C4—611no—
311C22×C4—611no—
312C22×C4—1222no—
313C22×C4—1222no—
314C22×C4—1222no—
315C22×C4—1222no—
316C22×C4—1222no—
317C22×C4—1222no—
318C22×C4—1222no—
319C22×C4—1222no—
320C22×C4—2441no—
321C22×C4—2441no—
322C22×C4—2441no—
323C22×C4C22×D6111yescharacteristic
324C22×C4C22×D6111yescharacteristic
325C22×C4C22×D6111yescharacteristic
326C22×C4C22×D6111yescharacteristic
327C22×C4C22×D6111yescharacteristic
328C4⋊C4—614no—
329C4⋊C4—614no—
330C4⋊C4—1222no—
331C4⋊C4—1222no—
332C4⋊C4—1222no—
333C4⋊C4—1222no—
334C4⋊C4—1222no—
335C22⋊C4—22no—
336C22⋊C4—22no—
337C22⋊C4—41no—
338C22⋊C4—614no—
339C22⋊C4—614no—
340C22⋊C4—614no—
341C22⋊C4—1222no—
342C22⋊C4—1222no—
343C22⋊C4—1222no—
344C22⋊C4—2441no—
345C42—1222no—
346C42—1222no—
347C42—1222no—
348C42—1222no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—612no—
360C23—1221no—
361C23—1221no—
362C23—1221no—
363C23—1221no—
364C23—1221no—
365C23—1221no—
366C23C2×C4×D6112yes—
367C23C2×C4×D6112yes—
368C23D4×D6112yes—
369C23#1175822412yes—
370C23C23×D6111yescharacteristic
371D4—28no—
372D4—1228no—
373D4—1228no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—44no—
388C2×C4—612no—
389C2×C4—612no—
390C2×C4—612no—
391C2×C4—612no—
392C2×C4—612no—
393C2×C4—612no—
394C2×C4—612no—
395C2×C4—612no—
396C2×C4—1228no—
397C2×C4—1221no—
398C2×C4—1221no—
399C2×C4—1221no—
400C2×C4—1221no—
401C2×C4—1221no—
402C2×C4—1221no—
403C2×C4—1221no—
404C2×C4—1221no—
405C2×C4—1221no—
406C2×C4—1221no—
407C2×C4—1221no—
408C2×C4—1221no—
409C2×C4—1221no—
410C2×C4—2444no—
411C2×C4—2444no—
412C2×C4—2444no—
413C2×C4C2×C4×D6112yes—
414C2×C4D4×D6112yes—
415C22—22no—
416C22—22no—
417C22—22no—
418C22—22no—
419C22—22no—
420C22—22no—
421C22—22no—
422C22—22no—
423C22—22no—
424C22—41no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—1222no—
429C22—1222no—
430C22—1222no—
431C22—2441no—
432C22—2441no—
433C22—2441no—
434C22—2441no—
435C22#1451973714yescomplemented
436C22C22×C4×D6111yescharacteristic
437C22C2×D4×D6111yescharacteristic
438C22C2×D4×D6111yescharacteristic
439C22#41×D6111yescharacteristic
440C22C2×#1175822411yescharacteristic
441C22#1451982211yescharacteristic
442C22#1451982411yescharacteristic
443C4—22no—
444C4—22no—
445C4—41no—
446C4—41no—
447C4—41no—
448C4—614no—
449C4—1222no—
450C4—1222no—
451C4—1222no—
452C4—1222no—
453C4—1222no—
454C4—2441no—
455C2—24no—
456C2—42no—
457C2—2442no—
458C2C4×D4×D6111yescharacteristic
459C2C2×#1451973711yescharacteristic
460C2#1684024111yescharacteristic
461C2#1684039411yescharacteristic
462C2#1684041011yescharacteristic
463C2#1684041811yescharacteristic
464C2#1684045511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutatorC22×C61C23×C4
FittingC61×#386C2
socleC23×C61C24
hypercenter#386D61
hypocenterC61#2361
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #386

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×D4×Dic61C2semidirect
3. C2×C4×C22⋊D61C2semidirect
4. C2×#14519737C2semidirect
5. C22×#11758196C2semidirect
6. #16839662C2semidirect
7. #16839659C2semidirect
8. #16839656C2semidirect
9. #16839651C2semidirect
10. #16839639C2semidirect
11. #16839636C2semidirect
12. #16839634C2semidirect
13. #16839613C2semidirect
14. C22⋊C4×Dic61C2semidirect
15. C61×#386C2semidirect
22. #14519749C4semidirect
61. C2×D4×C61C2×C4semidirect
74. C2×C22⋊D61C2×C4semidirect
75. C2×C22⋊D61C2×C4semidirect
84. C22×Dic61C2×C4semidirect
99. C22⋊Dic61C2×C4semidirect
100. C22⋊Dic61D4semidirect
104. #11758198C2×C4semidirect
110. #11758196C2×C4semidirect
111. #11758196D4semidirect
195. C22×C61C4×D4semidirect
221. Dic61C4×D4semidirect
243. #386D61semidirect
248. C61#2361semidirect
300. C2×D4C4×D61semidirect
435. C22#14519737semidirect